Scatterometry-Based Imaging and Critical Dimension Metrology

ABSTRACT

Methods and systems for performing measurements of semiconductor structures and materials based on scatterometry measurement data are presented. Scatterometry measurement data is used to generate an image of a material property of a measured structure based on the measured intensities of the detected diffraction orders. In some examples, a value of a parameter of interest is determined directly from the map of the material property of the measurement target. In some other examples, the image is compared to structural characteristics estimated by a geometric, model-based parametric inversion of the same measurement data. Discrepancies are used to update the geometric model of the measured structure and improve measurement performance. This enables a metrology system to converge on an accurate parametric measurement model when there are significant deviations between the actual shape of a manufactured structure subject to model-based measurement and the modeled shape of the structure.

CROSS REFERENCE TO RELATED APPLICATION

The present application for patent claims priority under 35 U.S.C. §119from U.S. provisional patent application Ser. No. 61/982,183, entitled“X-Ray Imaging of Semiconductor Devices,” filed Apr. 21, 2014, and fromU.S. provisional patent application Ser. No. 61/982,326, entitled “X-RayImaging of Semiconductor Devices,” filed Apr. 22, 2014, the subjectmatter of each is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The described embodiments relate to metrology systems and methods, andmore particularly to methods and systems for improved measurementaccuracy.

BACKGROUND INFORMATION

Semiconductor devices such as logic and memory devices are typicallyfabricated by a sequence of processing steps applied to a specimen. Thevarious features and multiple structural levels of the semiconductordevices are formed by these processing steps. For example, lithographyamong others is one semiconductor fabrication process that involvesgenerating a pattern on a semiconductor wafer. Additional examples ofsemiconductor fabrication processes include, but are not limited to,chemical-mechanical polishing, etch, deposition, and ion implantation.Multiple semiconductor devices may be fabricated on a singlesemiconductor wafer and then separated into individual semiconductordevices.

Metrology processes are used at various steps during a semiconductormanufacturing process to detect defects on wafers to promote higheryield. A number of metrology based techniques including scatterometryand reflectometry implementations and associated analysis algorithms arecommonly used to characterize critical dimensions, film thicknesses,composition and other parameters of nanoscale structures.

Traditionally, scatterometry measurements are performed on targetsconsisting of thin films and/or repeated periodic structures. Duringdevice fabrication, these films and periodic structures typicallyrepresent the actual device geometry and material structure or anintermediate design. As devices (e.g., logic and memory devices) movetoward smaller nanometer-scale dimensions, characterization becomes moredifficult. Devices incorporating complex three-dimensional geometry andmaterials with diverse physical properties contribute tocharacterization difficulty. For example, modern memory structures areoften high-aspect ratio, three-dimensional structures that make itdifficult for optical radiation to penetrate to the bottom layers.Optical metrology tools utilizing infrared to visible light canpenetrate many layers of translucent materials, but longer wavelengthsthat provide good depth of penetration do not provide sufficientsensitivity to small anomalies. In addition, the increasing number ofparameters required to characterize complex structures (e.g., FinFETs),leads to increasing parameter correlation. As a result, the parameterscharacterizing the target often cannot be reliably decoupled withavailable measurements.

In another example, opaque, high-k materials are increasingly employedin modern semiconductor structures. Optical radiation is often unable topenetrate layers constructed of these materials. As a result,measurements with thin-film scatterometry tools such as ellipsometers orreflectometers are becoming increasingly challenging.

In response to these challenges, more complex optical metrology toolshave been developed. For example, tools with multiple angles ofillumination, shorter illumination wavelengths, broader ranges ofillumination wavelengths, and more complete information acquisition fromreflected signals (e.g., measuring multiple Mueller matrix elements inaddition to the more conventional reflectivity or ellipsometric signals)have been developed. However, these approaches have not reliablyovercome fundamental challenges associated with measurement of manyadvanced targets (e.g., complex 3D structures, structures smaller than10 nm, structures employing opaque materials) and measurementapplications (e.g., line edge roughness and line width roughnessmeasurements).

Atomic force microscopes (AFM) and scanning-tunneling microscopes (STM)are able to achieve atomic resolution, but they can only probe thesurface of the specimen. In addition, AFM and STM microscopes requirelong scanning times.

Scanning electron microscopes (SEM) achieve intermediate resolutionlevels, but are unable to penetrate structures to sufficient depth.Thus, high-aspect ratio holes are not characterized well. In addition,the required charging of the specimen has an adverse effect on imagingperformance.

Transmission electron microscopes (TEM) achieve high resolution levelsand are able to probe arbitrary depths, but TEM requires destructivesectioning of the specimen.

Small-Angle X-ray Scattering (SAXS) techniques have been shown toprovide sufficient resolution and depth of penetration. Model-basedinterpretation of SAXS data assumes a representative model of thegeometry and optical properties of the specimen. However, themeasurement model has limited degrees of freedom; typically much lessthan the degrees of freedom of the measured data. If the actual sampleis not accurately described by the measurement model, the resultingsolution to the model based optimization does not provide anyinformation concerning the source of the model mismatch. This makes itvery difficult to develop a measurement model that properlycharacterizes a specimen unless the structure of the specimen iswell-known a priori. This up-front knowledge of the specimen is oftenunavailable during process development

Future metrology applications present challenges for metrology due toincreasingly small resolution requirements, multi-parameter correlation,increasingly complex geometric structures, and increasing use of opaquematerials. Thus, methods and systems for improved CD measurements aredesired.

SUMMARY

Methods and systems for performing measurements of semiconductorstructures and materials based on scatterometry measurement data arepresented. Such systems are employed to measure structural and materialcharacteristics (e.g., material composition, dimensional characteristicsof structures, etc.) associated with different semiconductor fabricationprocesses.

More specifically, scatterometry measurement data is used to generate animage of a measured structure based on the measured intensities of thedetected diffraction orders. In some examples, the image is compared tostructural characteristics estimated by a geometric, model-basedparametric inversion of the same scatterometry measurement data.Discrepancies are used to update the geometric model of the measuredstructure and improve measurement performance. The ability to convergeon an accurate parametric measurement model is particularly importantwhen measuring integrated circuits to control, monitor, andtrouble-shoot their manufacturing process.

In one aspect, a computing system is configured to generate an model ofa material property of a measured structure and resolve an image of themeasured structure by performing a fitting analysis of scatterometrymeasurement data with the model. The model that describes the geometryand material parameters of the structure under measurement is afree-form model that does not include a preconceived geometry andmaterial distribution. In some embodiments, the model includes manysmall voxels (volumetric elements) that each have an independentlyadjustable material parameter value (e.g., electron density,absorptivity, or complex refractive index). In some other embodiments,the material properties are piecewise constant. The propertiesassociated with each different material are determined a priori. Theboundaries between different materials are free-form surfaces, and thesesurfaces can be determined by the level set algorithm.

In a further aspect, the same scatterometry data acquired for CDmetrology is used to calculate an image of the sample. In some examples,the image is a two dimensional (2-D) map of electron density,absorptivity, complex index of refraction, or a combination of thesematerial characteristics. In some examples, the image is a threedimensional (3-D) map of electron density, absorptivity, complex indexof refraction, or a combination of these material characteristics. Themap is generated using relatively few physical constraints. Theresulting map is generally unsuitable for measuring CD because it lackssufficient resolution. However, the map is useful for debugging thewafer process when the sample geometry or materials deviate outside therange of expected values contemplated by the geometric model employedfor CD measurement. In one example, the differences between the map anda rendering of the structure predicted by the geometric model accordingto its measured parameters are used to update the geometric model andimprove its measurement performance.

The foregoing is a summary and thus contains, by necessity,simplifications, generalizations and omissions of detail; consequently,those skilled in the art will appreciate that the summary isillustrative only and is not limiting in any way. Other aspects,inventive features, and advantages of the devices and/or processesdescribed herein will become apparent in the non-limiting detaileddescription set forth herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrative of a metrology system 100 configured toperform x-ray scatterometry measurements in accordance with the methodsdescribed herein.

FIG. 2 is a diagram illustrative of a metrology system 200 in anotherembodiment configured to perform scatterometry measurements inaccordance with the methods described herein.

FIG. 3 is a diagram illustrative of a metrology system 300 in anotherembodiment configured to perform grazing incidence scatterometrymeasurements in accordance with the methods described herein.

FIG. 4 is a diagram illustrative of a x-ray detector 116 of metrologysystems 100, 200, and 300 contained in a vacuum environment 162 separatefrom specimen 101.

FIG. 5 is a diagram illustrative of a model building and analysis engine120 configured to resolve a map of a material property of a measuredspecimen based on scatterometry measurement data in accordance with themethods described herein.

FIG. 6 is a diagram illustrative of a spatially discretized model of asemiconductor structure.

FIG. 7 is a diagram illustrative of a model building and analysis engine150 configured to resolve specimen parameter values based onscatterometry measurement data in accordance with the methods describedherein.

FIG. 8 is a flowchart illustrative of an exemplary method 400 ofdetermining a map of a material property of a measured specimen based onscatterometry measurements.

DETAILED DESCRIPTION

Reference will now be made in detail to background examples and someembodiments of the invention, examples of which are illustrated in theaccompanying drawings.

Methods and systems for performing measurements of semiconductorstructures and materials based on scatterometry measurement data arepresented. Such systems are employed to measure structural and materialcharacteristics (e.g., material composition, dimensional characteristicsof structures, etc.) associated with different semiconductor fabricationprocesses.

More specifically, scatterometry measurement data is used to generate animage of a measured structure based on the measured intensities of thedetected diffraction orders. In some examples, the image is compared tostructural characteristics estimated by a geometric, model-basedparametric inversion of the same scatterometry measurement data.Discrepancies are used to update the geometric model of the measuredstructure and improve measurement performance. The ability to convergeon an accurate parametric measurement model is particularly importantwhen measuring integrated circuits to control, monitor, andtrouble-shoot their manufacturing process.

Geometric, model-based, parametric inversion is preferred for criticaldimension (CD) metrology based on SAXS measurements. However, when themeasured specimen deviates from the assumptions of the geometric model,a map of the specimen generated from the same SAXS measurement data isuseful to identify and correct model errors.

The use of high brightness SAXS (in either grazing incidence ortransmission incidence configurations) enables high flux x-ray radiationpenetration into opaque areas of the target. Examples of measureablegeometric parameters using SAXS includes pore size, pore density, lineedge roughness, line width roughness, side wall angle, profile, criticaldimension, overlay, edge placement error, and pitch. Examples ofmeasureable material parameters include electron density, elementalidentification and composition. In some examples, SAXS enables themeasurement of features smaller than 10 nm as well as advancedsemiconductor structures such as spin-transfer-torque MRAM wheremeasurements of geometrical parameters and material parameters areneeded.

A SAXS measurement involves illuminating a sample with an X-ray beam anddetecting the intensities of the resulting diffraction orders formultiple angles of incidence relative to the sample, multiplewavelengths, or both. CD metrology based on SAXS involves determiningthe dimensions of the sample from the measurements by regression.Regression uses a pre-determined geometric model with a few (on theorder of ten) adjustable parameters. This reduces the uncertainty andincreases the speed of the CD measurement, but also limits the set ofpossible shapes contemplated by the model. During manufacture, orparticularly during process development, a specimen may fall outsidethis limited set of possible shapes. For example, a line may beunder-cut when the model does not include that possibility. In thiscase, the model will fail to capture this geometric feature. Inaddition, the measurement will provide no indication of the particularsource of this failure.

In one aspect, the same scatterometry data acquired for CD metrology isused to calculate an image of the sample. In some examples, the image isa two dimensional (2-D) map of electron density, absorptivity, complexindex of refraction, or a combination of these material characteristics.In some examples, the image is a three dimensional (3-D) map of electrondensity, absorptivity, complex index of refraction, or a combination ofthese material characteristics. The map is generated using relativelyfew physical constraints. In some examples, one or more parameters ofinterest, such as critical dimension (CD), sidewall angle (SWA),overlay, edge placement error, pitch walk, etc., are estimated directlyfrom the resulting map. In some other examples, the map is useful fordebugging the wafer process when the sample geometry or materialsdeviate outside the range of expected values contemplated by aparametric structural model employed for model-based CD measurement. Inone example, the differences between the map and a rendering of thestructure predicted by the parametric structural model according to itsmeasured parameters are used to update the parametric structural modeland improve its measurement performance.

FIG. 1 illustrates an embodiment of a metrology tool 100 for measuringcharacteristics of a specimen in accordance with the exemplary methodspresented herein. As shown in FIG. 1, the system 100 may be used toperform transmission SAXS measurements over an inspection area 102 of aspecimen 101 disposed on a specimen positioning system 140. In someembodiments, the inspection area 102 has a spot size of fiftymicrometers or less.

In the depicted embodiment, metrology tool 100 includes an x-rayillumination source 110 configured to generate x-ray radiation suitablefor SAXS measurements. In some embodiments, the x-ray illuminationsystem 110 is configured to generate wavelengths between 0.01 nanometersand 1 nanometer. X-ray illumination source 110 produces an x-ray beam117 incident on inspection area 102 of specimen 101.

In general, any suitable high-brightness x-ray illumination sourcecapable of generating high brightness x-rays at flux levels sufficientto enable high-throughput, inline metrology may be contemplated tosupply x-ray illumination for SAXS measurements. In some embodiments, anx-ray source includes a tunable monochromator that enables the x-raysource to deliver x-ray radiation at different, selectable wavelengths.

In some embodiments, one or more x-ray sources emitting radiation withphoton energy greater than 15 keV are employed. By way of non-limitingexample, any of a particle accelerator source, a liquid anode source, arotating anode source, a microfocus source, a microfocus rotating anodesource, and an inverse Compton source may be employed as x-ray source110. In one example, an inverse Compton source available from LynceanTechnologies, Inc., Palo Alto, Calif. (USA) may be contemplated. InverseCompton sources have an additional advantage of being able to producex-rays over a range of photon energies, thereby enabling the x-raysource to deliver x-ray radiation at different, selectable wavelengths.

Exemplary x-ray sources include electron beam sources configured tobombard solid or liquid targets to stimulate x-ray radiation. FIG. 2depicts a metrology tool 200 for measuring characteristics of a specimenin accordance with the exemplary methods presented herein. Like numberedelements of metrology tool 100 and 200 are analogous. However, in theembodiment depicted in FIG. 2, x-ray illumination source 110 is a liquidmetal based x-ray illumination system. A jet of liquid metal 119 isproduced from a liquid metal container 111 and collected in a liquidmetal collector 112. A liquid metal circulation system (not shown)returns liquid metal collected by collector 112 to liquid metalcontainer 111. The jet of liquid metal 119 includes one or moreelements. By way of non-limiting example, the jet of liquid metal 119includes any of Aluminum, Gallium, Indium, Tin, Thallium, and Bismuth.In this manner, the jet of liquid metal 119 produces x-ray linescorresponding with its constituent elements. In one embodiment, the jetof liquid metal includes a Gallium and Indium alloy. In someembodiments, the x-ray illumination system 110 is configured to generatewavelengths between 0.01 nanometers and 1 nanometer. An electron beamsource 113 (e.g., electron gun) produces a stream of electrons 118 thatis directed by electron optics 114 to the jet of liquid metal 119.Suitable electron optics 114 includes electromagnets, permanent magnets,or a combination of electromagnets and permanent magnets for focusingthe electron beam and directing the beam at the liquid metal jet. Thecoincidence of the jet of liquid metal 119 and the stream of electrons118 produces an x-ray beam 117 incident on inspection area 102 ofspecimen 101.

In one embodiment, the incident x-ray beam 117 is at the Indium kα lineof 24.2 keV. The x-ray beam is collimated down to less than onemilliradian divergence using multi-layer x-ray optics for transmissionSAXS measurements.

In some embodiments, the x-ray scattering measurements described hereinare achieved without using a screen located between the x-ray source andthe specimen under measurement. In these embodiments, the measuredintensities of the diffraction orders over a range of angles ofincidence, multiple wavelengths, or a combination of both, providesufficient information to resolve a distribution map (i.e., image) ofthe desired material property (e.g., complex refractive index, electrondensity, or absorptivity) of the measured structure. However, in someother examples, a pinhole or another aperture in located on an otherwiseopaque screen that is located between the x-ray source and the specimenunder measurement to improve collimation of the x-ray beam. Theintensity of the diffraction pattern is measured for several positionsof the aperture. In some other embodiments, a screen with apseudo-random aperture pattern is used, and the diffraction pattern ismeasured for multiple screens. These approaches may also be contemplatedto provide additional information to resolve the three-dimensionaldistribution of the desired material property of the measured structure.

Methods and systems for generating high brightness, liquid metal x-rayillumination are described in U.S. Pat. No. 7,929,667, issued on Apr.19, 2011, to KLA-Tencor Corp., the entirety of which is incorporatedherein by reference.

As depicted in FIG. 1, x-ray optics 115 shape and direct incident x-raybeam 117 to specimen 101. In some examples, x-ray optics 115 include anx-ray monochromator to monochromatize the x-ray beam that is incident onthe specimen 101. In one example, a crystal monochromator such as aLoxley-Tanner-Bowen monochromator is employed to monochromatize the beamof x-ray radiation. In some examples, x-ray optics 115 collimate orfocus the x-ray beam 117 onto inspection area 102 of specimen 101 toless than 1 milliradian divergence using multilayer x-ray optics. Insome embodiments, x-ray optics 115 includes one or more x-raycollimating mirrors, x-ray apertures, x-ray beam stops, refractive x-rayoptics, diffractive optics such as zone plates, specular x-ray opticssuch as grazing incidence ellipsoidal mirrors, polycapillary optics suchas hollow capillary x-ray waveguides, multilayer optics, or systems, orany combination thereof.

X-ray detector 116 collects x-ray radiation 125 scattered from specimen101 and generates an output signal 126 indicative of properties ofspecimen 101 that are sensitive to the incident x-ray radiation inaccordance with a SAXS measurement modality. In some embodiments,scattered x-rays 125 are collected by x-ray detector 116 while specimenpositioning system 140 locates and orients specimen 101 to produceangularly resolved scattered x-rays. In some embodiments, the x-raydetector 116 is able to resolve one or more x-ray photon energies andproduces signals for each x-ray energy component indicative ofproperties of the specimen. In some embodiments, the x-ray detector 116includes any of a CCD array, a microchannel plate, a photodiode array, amicrostrip proportional counter, a gas filled proportional counter, ascintillator, or a fluorescent material. In some embodiments, the x-raydetector 116 includes a single photon counting detector that detects theposition and number of detected photons.

In some embodiments, x-ray detector 116 is maintained in the sameatmospheric environment as specimen 101 (e.g., gas purge environment).However, in some embodiments, the distance between specimen 101 andx-ray detector 116 is lengthy (e.g., greater than one meter). In theseembodiments, environmental disturbances (e.g., air turbulence)contribute noise to the detected signals. Hence in some embodiments, oneor more of the x-ray detectors is maintained in a localized, vacuumenvironment separated from the specimen (e.g., specimen 101) by a vacuumwindow.

FIG. 4 is a diagram illustrative of a vacuum chamber 160 containingx-ray detector 116 in one embodiment. In a preferred embodiment, vacuumchamber 160 includes a substantial portion of the path between specimen101 and x-ray detector 116. An opening of vacuum chamber 160 is coveredby vacuum window 161. Vacuum window 161 may be constructed of anysuitable material that is substantially transparent to x-ray radiation(e.g., Beryllium). Scattered x-ray radiation 125 passes through vacuumwindow 161, enters vacuum chamber 160 and is incident on x-ray detector116. A suitable vacuum environment 162 is maintained within vacuumchamber 160 to minimize disturbances to scattered x-ray radiation 125.

FIG. 3 illustrates an x-ray metrology system 300 for performingsemiconductor metrology measurements in accordance with the methodsdescribed herein. As illustrated in FIG. 3, x-ray metrology system 300includes similar, like numbered elements described with reference toFIGS. 1 and 2. However, x-ray metrology system 300 operates in a grazingincidence mode. More specifically, x-ray metrology system 300 isconfigured as a grazing incidence small-angle x-ray scattering (GISAXS)measurement system. Typical angles of incidence and collection areapproximately one degree as measured from the surface of the specimen,or approximately eighty nine degrees from an axis normal to the surfaceof the specimen. X-ray metrology system 300 is configured such thatx-rays scattered from the specimen are collected by a detector while asample handler (not shown) positions the specimen. In addition, anyother particles produced during the interaction such as photoelectrons,x-rays produced through fluorescence, or ions can be detected. Metrologysystems configured to perform GISAXS measurements require a highbrightness x-ray source to maintain sufficient brightness over therelatively large sample area illuminated at small angles. For thisreason, a liquid metal jet x-ray source 110 described with reference toFIG. 2 is particularly well suited for GISAXS measurements.

By way of non-limiting example, the x-ray metrology systems 100 and 200illustrated in FIGS. 1 and 2, respectively, are configured astransmission small angle x-ray scatterometers (TSAXS) and the x-raymetrology system 300 illustrated in FIG. 3 is configured as a grazingincidence small angle x-ray scatterometer (GISAXS). However, in general,an x-ray metrology system configured to perform scatterometry basedmeasurements and generate images as described herein may employ any oneor more of the following metrology techniques: transmission small anglex-ray scattering (TSAXS), grazing incidence small angle x-ray scattering(GISAXS), wide angle x-ray scattering (WAXS), x-ray reflectivity (XRR),x-ray diffraction (XRD), grazing incidence x-ray diffraction (GIXRD),high resolution x-ray diffraction (HRXRD), x-ray photoelectronspectroscopy (XPS), x-ray fluorescence (XRF), grazing incidence x-rayfluorescence (GIXRF), x-ray tomography, x-ray ellipsometry, and hardx-ray photoemission spectrometry (HXPS).

Metrology tool 100 also includes a computing system 130 employed toacquire signals 126 generated by SAXS detector 116 and determineproperties of the specimen based at least in part on the acquiredsignals. As illustrated in FIG. 1, computing system 130 iscommunicatively coupled to SAXS detector 116.

In a further embodiment, computing system 130 is configured to accessmodel parameters in real-time, employing Real Time Critical Dimensioning(RTCD), or it may access libraries of pre-computed models fordetermining a value of at least one specimen parameter value associatedwith the specimen 101. In general, some form of CD-engine may be used toevaluate the difference between assigned CD parameters of a specimen andCD parameters associated with the measured specimen. Exemplary methodsand systems for computing specimen parameter values are described inU.S. Pat. No. 7,826,071, issued on Nov. 2, 2010, to KLA-Tencor Corp.,the entirety of which is incorporated herein by reference.

In one further aspect, metrology tool 100 includes a computing system(e.g., computing system 130) configured to implement beam controlfunctionality as described herein. In the embodiment depicted in FIG. 1,computing system 130 is configured as a beam controller operable tocontrol any of the illumination properties such as intensity,divergence, spot size, polarization, spectrum, and positioning of theincident SAXS illumination beam 117.

As illustrated in FIG. 1, computing system 130 is communicativelycoupled to SAXS detector 116. Computing system 130 is configured toreceive measurement data 126 from SAXS detector 116. In one example,measurement data 126 includes an indication of the measured SAXSresponse of the specimen (i.e., intensities of the diffraction orders).Based on the distribution of the measured SAXS response on the surfaceof detector 116, the location and area of incidence of SAXS illuminationbeam 117 on specimen 101 is determined by computing system 130. In oneexample, pattern recognition techniques are applied by computing system130 to determine the location and area of incidence of SAXS illuminationbeam 117 on specimen 101 based on measurement data 126. In someexamples, computing system 130 communicates command signal 137 toillumination optics 115 to select the desired illumination wavelengthand redirect and reshape SAXS illumination beam 117 such that incidentSAXS illumination beam 117 arrives at the desired location and angularorientation with respect to specimen 101. In some other examples,computing system 130 communicates a command signal to wafer positioningsystem 140 to position and orient specimen 101 such that incident SAXSillumination beam 117 arrives at the desired location and angularorientation with respect to specimen 101. In some other examples,computing system 130 communicates a command signal 137 to x-ray source110 to select the desired illumination wavelength and redirect andreshape SAXS illumination beam 117 such that incident SAXS illuminationbeam 117 arrives at the desired location and angular orientation withrespect to specimen 101.

In another aspect, SAXS measurements of a particular inspection area areperformed at a number of different angles of incidence. In someembodiments, it is desirable to perform measurements at different anglesof incidence described by rotations about the x and y axes indicated bycoordinate system 146 depicted in FIG. 1. This increases the precisionand accuracy of measured parameters and reduces correlations amongparameters by extending the number and diversity of data sets availablefor analysis to include a variety of large-angle, out of planeorientations. Measuring specimen parameters with a deeper, more diversedata set also reduces correlations among parameters and improvesmeasurement accuracy. For example, in a normal orientation, SAXS is ableto resolve the critical dimension of a feature, but is largelyinsensitive to sidewall angle and height of a feature. However, bycollecting measurement data over a broad range of out of plane angularpositions, the sidewall angle and height of a feature can be resolved.

As illustrated in FIG. 1, metrology tool 100 includes a specimenpositioning system 140 configured to both align specimen 101 and orientspecimen 101 over a large range of out of plane angular orientationswith respect the SAXS scatterometer. In other words, specimenpositioning system 140 is configured to rotate specimen 101 over a largeangular range about one or more axes of rotation aligned in-plane withthe surface of specimen 101. In some embodiments, specimen positioningsystem 140 is configured to rotate specimen 101 within a range of atleast 90 degrees about one or more axes of rotation aligned in-planewith the surface of specimen 101. In some embodiments, specimenpositioning system is configured to rotate specimen 101 within a rangeof at least 60 degrees about one or more axes of rotation alignedin-plane with the surface of specimen 101. In some other embodiments,specimen positioning system is configured to rotate specimen 101 withina range of at least one degree about one or more axes of rotationaligned in-plane with the surface of specimen 101. In this manner, angleresolved measurements of specimen 101 are collected by metrology system100 over any number of locations on the surface of specimen 101. In oneexample, computing system 130 communicates command signals to motioncontroller 145 of specimen positioning system 140 that indicate thedesired position of specimen 101. In response, motion controller 145generates command signals to the various actuators of specimenpositioning system 140 to achieve the desired positioning of specimen101.

By way of non-limiting example, as illustrated in FIG. 1, specimenpositioning system 140 includes an edge grip chuck 141 to fixedly attachspecimen 101 to specimen positioning system 140. A rotational actuator142 is configured to rotate edge grip chuck 141 and the attachedspecimen 101 with respect to a perimeter frame 143. In the depictedembodiment, rotational actuator 142 is configured to rotate specimen 101about the x-axis of the coordinate system 146 illustrated in FIG. 1. Asdepicted in FIG. 1, a rotation of specimen 101 about the z-axis is an inplane rotation of specimen 101. Rotations about the x-axis and they-axis (not shown) are out of plane rotations of specimen 101 thateffectively tilt the surface of the specimen with respect to themetrology elements of metrology system 100. Although it is notillustrated, a second rotational actuator is configured to rotatespecimen 101 about the y-axis. A linear actuator 144 is configured totranslate perimeter frame 143 in the x-direction. Another linearactuator (not shown) is configured to translate perimeter frame 143 inthe y-direction. In this manner, every location on the surface ofspecimen 101 is available for measurement over a range of out of planeangular positions. For example, in one embodiment, a location ofspecimen 101 is measured over several angular increments within a rangeof −45 degrees to +45 degrees with respect to the normal orientation ofspecimen 101.

In general, specimen positioning system 140 may include any suitablecombination of mechanical elements to achieve the desired linear andangular positioning performance, including, but not limited togoniometer stages, hexapod stages, angular stages, and linear stages.

In one aspect, metrology tool 100 includes a computing system configuredto generate a free-form model of a material property of a measuredstructure and resolve an image of the measured structure by performing afitting analysis of scatterometry measurement data with the model. Themodel that describes the geometry and material parameters of thestructure under measurement is a free-form model that does not include apreconceived geometry and material distribution. In some embodiments,the model includes many small voxels (volumetric elements) that eachhave an independently adjustable material parameter value (e.g.,electron density, absorptivity, or complex refractive index). In someother embodiments, the material properties are piecewise constant. Theproperties associated with each different material are determined apriori. The boundaries between different materials are free-formsurfaces, and these surfaces can be determined by the level setalgorithm.

By way of non-limiting example, the material property may be electrondensity, absorptivity, or complex index of refraction of the structure.However, in general, other material properties may be contemplated. Insome embodiments, the measured structure is a device constructed on awafer. In a preferred embodiment, the structure is spatially periodic inone or more directions aligned with the wafer surface. In some examples,the periodic structure is repeated in one dimension (e.g., x-direction)and extends uniformly in the other in-plane dimension (e.g.,y-direction). In these examples, the free-form model is atwo-dimensional model (i.e., area model). In these examples, areaelements are employed to generate a two-dimensional image of thestructure in the relevant directions (e.g., x-direction andz-direction). In these examples, the third dimension (e.g., y-direction)is uniform and redundant. In other examples, the periodic structure isrepeated in an orthogonal or non-orthogonal pattern. In these examples,the free-form model is a three-dimensional model (i.e., volumetricmodel). In these examples, volume elements are employed to generate athree-dimensional image of the structure in the relevant directions(e.g., x-direction, y-direction, and z-direction). In some examples, theperiodic structure is a dedicated metrology target placed in a scribeline between dies. In some other examples, the periodic structure islocated in the active die area and is a part of a functional integratedcircuit (e.g., memory, image sensor, logic device, etc.).

In the embodiment depicted in FIG. 1, computing system 130 is configuredas model building and analysis engine 120 and is operable to implementmodel building and analysis functionality as described herein.

FIG. 5 is a diagram illustrative of model building and analysis engine120 configured to resolve an image of a material property of a measuredspecimen based on scatterometry measurement data in accordance with themethods described herein. As depicted in FIG. 5, model building andanalysis engine 120 includes an image building module 121 that generatesan image 122 of a property of the measured structure.

In one embodiment, image building module 121 generates a complex-valuedmap of the refractive index of the measured structure, n(x,y,z). Thecomplex refractive index corresponds to a particular electron densityand a particular absorption cross-section. In one embodiment, the map ofthe complex refractive index is represented by complex numbers assignedto volume elements (voxels) representative of the measured structure.FIG. 6 depicts a periodic semiconductor structure 170 that is spatiallydiscretized by a three dimensional array of voxels 171. Voxels 173 thatcorrespond with the structure itself are shaded in FIG. 6. Voxels 172that surround the structure 170 and may include different materials(e.g., air) are not shaded in FIG. 6. Each voxel is assigned an initialvalue for the expected complex index of refraction associated with thematerial within each voxel. In this example, image building module 121generates a three dimensional image 122 of the complex index ofrefraction of the measured structure 170. In another embodiment, the mapof the complex refractive index is represented by complex numbersassigned to area elements (pixels) representative of the measuredstructure. Each pixel is assigned an initial value for the expectedcomplex index of refraction associated with the material within eachpixel. In these examples, image building module 121 generates a twodimensional image of the complex index of refraction of the measuredstructure.

The voxels employed to describe the volume of the structure may beuniform, or may have irregular shapes and size. Furthermore, during thecourse of optimization, the shape of the voxels may be changed, e.g.,subdivided or consolidated, so as to render the shape more realistic orto increase the speed of the optimization. When using non-uniformvoxels, care must be taken to normalize functionals, such as thediscrete spatial derivative, relative to the size or shape of the voxel.Similarly, pixels employed to describe the area of a structure (e.g.,when the free-form model is two-dimensional) may be modified duringoptimization.

In some other embodiments, each map can be represented as a linearcombination of pre-determined basis functions, the linear combinationhaving complex coefficients. In another embodiment, the morphology ofthe specimen is optimized to fit the scatterometry data while takingadvantage of properties of materials that are known to constitute thespecimen. Each material boundary is represented by a level set{(x,y,z)|φ(x,y,z)=0} of a function, φ, of position. The functionφ(x,y,z) does not indicate any physical property of the specimen at thepoint (x,y,z). Its level set indicates the geometry of a materialboundary. Material properties in the interior of the level set areassigned constant values that are measured or calculated a priori forbulk materials. The optimization algorithm makes iterative changes tofunction φ in order to fit the scatterometry data. The function φ can berepresented by its samples on a mesh or by a linear combination of basisfunctions.

Although, a map of the complex index of refraction is described withreference to FIG. 6, a map of other material properties (e.g., electrondensity, absorptivity, etc.) may be contemplated.

The map 122 and the measured intensities of the diffraction orders 126are received as input to fitting analysis module 123. In general,measurement signals 126 communicated to fitting analysis module 123 mayinclude data associated with any combination of angle-resolved andwavelength-resolved SAXS measurements.

In a preferred embodiment the measured intensities are angle-resolved,i.e., the intensities of diffraction orders are measured for multiplevalues of m and n for many orientations of the wafer. In someembodiments, the wafer is held by a 6-axis stage that can translate andorient the wafer at the desired measurement positions with respect tothe incoming beam. In some other embodiments, the wafer may be heldfixed, or limited to a subset of the desired positions, and thedirection of incidence of the beam of x-ray radiation is changed usingmoveable x-ray optics such as grazing incidence mirrors or a Fresnelzone-plate.

In another embodiment, the measured intensities are wavelength-resolved.In this embodiment, the polar angles of incidence, q and j, are heldconstant and measurements are taken for different wavelengths of theincident x-ray radiation. The wavelength can be changed by passingbroadband light through an adjustable monochromator.

In the SAXS measurement, a periodic structure (e.g., structure 170)diffracts a collimated X-ray beam into diffraction orders. Eachdiffraction order travels in a particular, predictable direction. Theangular spacing of the diffraction orders is inversely proportional tothe lattice constant of the specimen divided by the wavelength. Thediffraction orders can be individually detected by a detector arrayplaced at some distance from the wafer. Each pixel of the detectoroutputs a signal that indicates the number of photons that hit thepixel. Outputs of pixels that belong to the same diffraction order arecombined. The intensities of diffraction orders are of the form I(m,nq,j,λ). {m,n} are integer indices of diffraction orders. {q,j} areazimuth and elevation angles of incidence beam (i.e., polar coordinatesof the incident chief ray with respect to a coordinate system that isfixed to the wafer. λ is the wavelength of the incident X-ray.

Fitting analysis module 123 receives the measurement signals 126indicative of the measured intensities of the diffraction orders andrefines the map 122 of the material property of the measured structurebased on the measured data. In some examples, the fitting analysis is aniterative optimization that involves minimizing differences between themeasured intensities of the diffraction orders and calculatedintensities.

In this example, the intensities of the diffraction orders arecalculated from the current estimate of the map of the refractive indexusing the first Born approximation. The approximation is described ingreater detail in Principles of optics, Max Born and Emil Wolf, 7th Ed.Cambridge University Press, 1999, the subject matter of which isincorporated herein by reference it its entirety.

According to the Born-approximation, for an incident x-ray field,u_(inc), the scattered X-ray field, u_(sca), is a solution to theinhomogeneous Helmholtz equation as illustrated in equation (1).

∇² u _(sca) +k ₀ ² u _(sca)=2k ₀ ²(α−iβ)u _(inc)

k ₀=2π/λ  (1)

The position-dependent refractive index of the sample in complexnotation is illustrated in equation (2).

α(x,y,z)−iβ(x,y,z)=1−n(x,y,z)  (2)

For energies above approximately 10 keV, α and β are simple functions ofthe classical electron radius, r_(e), atomic photo-absorption crosssection σ_(a), the wavelength λ, atomic number Z, and the electrondensity ρ as described in equations (3) and (4).

$\begin{matrix}{{\alpha \left( {x,y,z} \right)} = {\frac{r_{e}\lambda^{2}}{2\pi}{\rho \left( {x,y,z} \right)}}} & (3) \\{{\beta \left( {x,y,z} \right)} = {\frac{\sigma_{a}\lambda}{4\pi \; Z}{\rho \left( {x,y,z} \right)}}} & (4)\end{matrix}$

For a periodic, two-dimensional lattice pattern with a unit-cell of size(Δx, Δy), equation (5) expresses the refractive index as a Fourierseries.

$\begin{matrix}{{{{\alpha \left( {x,y,z} \right)} - {{\beta}\left( {x,y,z} \right)}} = {\sum\limits_{m,n}\; {{c_{m,n}(z)}{\exp \left( {\; {K_{m,n} \cdot \left( {x,y} \right)}} \right)}}}}{K_{m,n} = \left( {\frac{2\pi \; m}{\Lambda_{x}},\frac{2\pi \; n}{\Lambda_{y}}} \right)}} & (5)\end{matrix}$

Equation (1) is solved exactly using the Green's function for Helmholtzequation as expressed in equation (6).

$\begin{matrix}{{{u_{sca}\left( {x,y,z} \right)} = {\sum\limits_{m,n}\; {{\exp \left( {{\; q_{x,m}x} + {\; q_{y,n}y} + {\; q_{z,m,n}z}} \right)}\frac{{\hat{c}}_{m,n}\left( \gamma_{m,n} \right)}{\; q_{z,m,n}}}}}{q_{x,m} = {\frac{2\pi \; m}{\Lambda_{x}} + {k_{0}\sin \; \theta \; \cos \; \varphi}}}{q_{y,n} = {\frac{2\pi \; n}{\Lambda_{x}} + {k_{0}\sin \; \theta \; \sin \; \varphi}}}{q_{z,m,n} = \sqrt{k_{0}^{2} - q_{x,m}^{2} - q_{y,n}^{2}}}{\xi_{m,n} = {\left( \frac{\lambda \; m}{\Lambda_{x}} \right)^{2} + \left( \frac{\lambda \; n}{\Lambda_{y}} \right)^{2} + {2\lambda \; \sin \; {\theta \left( {\frac{m\; \cos \; \varphi}{\Lambda_{x}} + \frac{n\; \sin \; \varphi}{\Lambda_{y}}} \right)}}}}{\gamma_{m,n} = {k_{0}\frac{\xi_{m,n}}{{\cos \; \theta} + \sqrt{{\cos \; \theta} - \xi_{m,n}}}}}{{{\hat{c}}_{m,n}\left( \gamma_{m,n} \right)} \equiv {\int{{c_{m,n}(z)}{\exp \left( {{\gamma}\; z} \right)}{z}}}}} & (6)\end{matrix}$

The scattered field, u_(sca), is a discrete sum of plane waves(diffraction orders). The intensity of the diffraction orders is|ĉ_(m,n)(γ)|².

Fitting analysis module 123 calculates the intensities of thediffraction orders from the current estimate of the map of therefractive index 122. At the first iteration, the intensities of thediffraction orders are calculated from the values of the refractiveindex of map 122. Module 123 generates a vector of differences betweenmeasured and calculated intensities of diffraction orders. Each entry ofthe difference vector pertains to a particular diffraction order m,n, aparticular orientation of the wafer, and a particular wavelength. Thecurrent estimate of the map is refined in a way to reduce a norm of thedifference vector using a non-linear minimization algorithm. In apreferred embodiment, the L2-norm is employed, however other norms maybe contemplated (e.g., L1-norm, etc.).

A variety of non-linear, constrained, or a combination of non-linear andconstrained optimization algorithms may be employed to iterativelyrefine the image. Preferred non-linear minimization algorithms includethe Levenberg-Marquardt algorithm, Gauss-Newton algorithm, SequentialQuadratic Programming algorithm, and the quasi-Newton algorithm. Furtherdetails are described in Practical Optimization, Gill, Murray, andWright, Emerald Publishing, 1982 and Numerical Methods for UnconstrainedOptimization and Nonlinear Equations, Dennis and Schnabel, Soc. forIndustrial & Applied Math., 1996, the subject matter of each isincorporated herein in its entirety. In some other embodiments, convexoptimization such as convex and interior point methods may be employed.Further details are described in Convex Optimization, Boyd andVandenberghe, Cambridge University Press, 2004, the subject matter ofwhich is incorporated herein in its entirety.

To facilitate convergence of the optimization, a number of constraintsmay be introduced into the optimization. By way of non-limiting example,the optimization may be subject to any of the following constraints: theelectron density cannot be negative, the absorption cannot be negative,the electron density and absorption cross-section have upper bounds forall materials, and the physical extent of the features under test haveknown upper and lower limits in the direction perpendicular to the waferplane.

In another example, the absorption is ignored and the mapping is reducedto a mapping of electron density only. For many semiconductor materials,such as silicon or tungsten, the absorption coefficient, β, is an orderof magnitude smaller than the scattering coefficient, a, at x-rayenergies near or above 10 keV. Thus, the contribution of absorption tothe measurement analysis can be safely ignored in many applications.

In a further aspect, the map is regularized by a norm of a functional ofthe complex refractive index. In some embodiments, the map isregularized by a norm of the value of the complex refractive index, itsfirst derivative or its discrete counterpart, its second derivative orits discrete counterpart, or any combination of these. In one example,the total variation (i.e., the L1-norm) of the gradient of the complexrefractive index is also included in the optimization cost function. Inone example, the optimization cost function to be minimized with respectto n(x,y,z) includes the L2-norm of intensity difference and the totalvariation of the discrete gradient of n as illustrated in expression(7).

$\begin{matrix}{{\sum\limits_{m,n}\; {\sum\limits_{\theta,\phi}\; {\sum\limits_{\lambda}\; \left\lbrack {{I_{MEASURED}\left( {m,n,\theta,\phi,\lambda} \right)} - {I_{CALCULATED}\left( {m,n,\theta,\phi,\lambda} \right)}} \right\rbrack^{2}}}} + {\mu {\sum\limits_{x,y,z}\; \left\lbrack {{\frac{\partial n}{\partial x}} + {\frac{\partial n}{\partial y}} + {\frac{\partial n}{\partial z}}} \right\rbrack}}} & (7)\end{matrix}$

The amount of regularization is controlled by the non-negative factor μ.In another example, the optimization cost function to be minimized withrespect to n(x,y,z) includes a norm of the gradient of the complex indexof refraction, and the optimization is subject to an upper bound on thevalue of a norm of the difference between the detected intensities ofthe diffraction orders and the estimated intensities of the diffractionorders.

In some other embodiments, a two-step optimization is employed. In oneexample, an optimization cost function that includes the L2-norm ofdifferences between the measured and calculated intensities is minimizedwith respect to n(x,y,z) until a threshold error value is achieved. Atthis point, a different optimization cost function that includes a normof the gradient of the complex refractive index is employed to furtherrefine the image of the property (e.g., electron density) of themeasured structure.

In some embodiments, two mixed norm optimizations are applied. In someexamples, an L2-norm is applied to the intensity error (called a Fitmeasure) and an L1-norm is applied to a functional of the index ofrefraction (called an Entropy Measure). These examples are provided byway of illustration. Many other examples within the discipline ofCompressed Sensing and/or Optimization Regularization may becontemplated. It is also contemplated that other techniques such asAkaike Information Criteria (AIC)/Bayesian Information Criteria (BIC),Ridge Regression, Basis Pursuit, Dantzig Selector, Rudin-Osher_Fatemi,Potts, Regularized Least Absolute Deviations (RLAD), SLOPE, and othersmay be applied.

Some examples have been provided that employ the L2 or L1 norms.However, it should be noted that any Lp norm, appropriate pseudo-normsuch as the L0 norm, or statistical measure, such as Entropy orKullbeck-Leibler divergence, may be applicable in the aforementionedexamples.

In addition to Lp-norms, measures based on these norms, but modified torender them differentiable, such as the Huber or pseudo-Huber lossfunction, may also be applied. These techniques and others practiced inthe field of robust regression are contemplated within the scope of thispatent document.

After convergence of the iterative optimization, the refined map 128 ofthe property of the measured structure is stored in a memory 190.

In one further aspect, one or more parameters of interest, such ascritical dimension (CD), sidewall angle (SWA), overlay, edge placementerror, pitch walk, etc., are estimated directly from the resulting map.In some embodiments, the resulting map is rendered on a display deviceand a user is able to select a parameter of interest directly from theimage. In response, computing system 130 is configured to determine thevalues of the selected parameter of interest. In some embodiments, theresulting map is analyzed automatically by computing system 130 toidentify values of a parameter of interest directly from the image.

In another further aspect, metrology tool 100 includes a computingsystem configured to generate a structural model (e.g., geometric model,material model, or combined geometric and material model) of a measuredstructure of a specimen, generate a SAXS response model that includes atleast one geometric parameter from the structural model, and resolve atleast one specimen parameter value by performing a fitting analysis ofSAXS measurement data with the SAXS response model. The analysis engineis used to compare the simulated SAXS signals with measured data therebyallowing the determination of geometric as well as material propertiessuch as electron density and elemental identification and composition ofthe sample. In the embodiment depicted in FIG. 1, computing system 130is configured as a model building and analysis engine configured toimplement model building and analysis functionality as described herein.

FIG. 7 is a diagram illustrative of an exemplary model building andanalysis engine 150 implemented by computing system 130. As depicted inFIG. 7, model building and analysis engine 150 includes a structuralmodel building module 151 that generates a structural model 152 of ameasured structure of a specimen. In some embodiments, structural model152 also includes material properties of the specimen. The structuralmodel 152 is received as input to SAXS response function building module153. SAXS response function building module 153 generates a SAXSresponse function model 155 based at least in part on the structuralmodel 152. In some examples, the SAXS response function model 155 isbased on x-ray form factors

F({right arrow over (q)})=∫ρ({right arrow over (r)})e^(−i{right arrow over (q)}·{right arrow over (r)}) d{right arrow over(r)}  (8)

where F is the form factor, q is the scattering vector, and ρ(r) is theelectron density of the specimen in spherical coordinates. The x-rayscattering intensity is then given by

I({right arrow over (q)})=F*F.  (9)

SAXS response function model 155 is received as input to fittinganalysis module 157. The fitting analysis module 157 compares themodeled SAXS response with the corresponding measured data to determinegeometric as well as material properties of the specimen.

In some examples, the fitting of modeled data to experimental data isachieved by minimizing a chi-squared value. For example, for SAXSmeasurements, a chi-squared value can be defined as

$\begin{matrix}{\chi_{SAXS}^{2} = {\frac{1}{N_{SAXS}}{\sum\limits_{j}^{N_{SAXS}}\; \frac{\left( {{S_{j}^{{SAXS}\mspace{14mu} {model}}\left( {v_{1},\ldots \mspace{14mu},v_{L}} \right)} - S_{j}^{{SAXS}\mspace{14mu} {experiment}}} \right)^{2}}{\sigma_{{SAXS},j}^{2}}}}} & (10)\end{matrix}$

Where, S_(j) ^(SAXS experiment) is the measured SAXS signals 126 in the“channel” j, where the index j describes a set of system parameters suchas diffraction order, energy, angular coordinate, etc. S_(j)^(SAXS model) (V₁, . . . , V_(L)) is the modeled SAXS signal S_(j) forthe “channel” j, evaluated for a set of structure (target) parametersV₁, . . . , V_(L), where these parameters describe geometric (CD,sidewall angle, overlay, etc.) and material (electron density, etc.).σ_(SAXS,j) is the uncertainty associated with the jth channel. N_(SAXS)is the total number of channels in the x-ray metrology. L is the numberof parameters characterizing the metrology target.

Equation (10) assumes that the uncertainties associated with differentchannels are uncorrelated. In examples where the uncertaintiesassociated with the different channels are correlated, a covariancebetween the uncertainties, can be calculated. In these examples achi-squared value for SAXS measurements can be expressed as

$\begin{matrix}{\chi_{SAXS}^{2} = {\frac{1}{N_{SAXS}}\left( {{{\overset{\rightarrow}{S}}_{j}^{{SAXS}.\mspace{14mu} {model}}\left( {v_{1},\ldots \mspace{14mu},v_{M}} \right)} - {\overset{\rightarrow}{S}}_{j}^{{SAXS}.\mspace{14mu} {experiment}}} \right)^{T}{V_{SAXS}^{- 1}\left( {{{\overset{\rightarrow}{S}}_{j}^{{SAXS}.\mspace{14mu} {model}}\left( {v_{1},\ldots \mspace{14mu},v_{M}} \right)} - {\overset{\rightarrow}{S}}_{j}^{{SAXS}.\mspace{14mu} {experiment}}} \right)}}} & (11)\end{matrix}$

where, V_(SAXS) is the covariance matrix of the SAXS channeluncertainties, and T denotes the transpose.

In some examples, fitting analysis module 157 resolves at least onespecimen parameter value by performing a fitting analysis on SAXSmeasurement data 126 with the SAXS response model 155. In some examples,X_(SAXS) ² is optimized.

SAXS metrologies may contain more than one respective technology whencalculating chi-squared values. For example, X_(SAXS) ² may becalculated for the combined use of grazing incidence SAXS andtransmission SAXS with a weight coefficient given to each technology.

As described hereinbefore, the fitting of SAXS data is achieved byminimization of chi-squared values. However, in general, the fitting ofSAXS data may be achieved by other functions.

The fitting of SAXS metrology data is advantageous for any type of SAXStechnology that provides sensitivity to geometric and/or materialparameters of interest. Specimen parameters can be deterministic (e.g.,CD, SWA, etc.) or statistical (e.g., rms height of sidewall roughness,roughness correlation length, etc.) as long as proper models describingSAXS beam interaction with the specimen are used.

Model building and analysis engine 150 improves the accuracy of measuredparameters by any combination of feed sideways analysis, feed forwardanalysis, and parallel analysis. Feed sideways analysis refers to takingmultiple data sets on different areas of the same specimen and passingcommon parameters determined from the first dataset onto the seconddataset for analysis. Feed forward analysis refers to taking data setson different specimens and passing common parameters forward tosubsequent analyses using a stepwise copy exact parameter feed forwardapproach. Parallel analysis refers to the parallel or concurrentapplication of a non-linear fitting methodology to multiple datasetswhere at least one common parameter is coupled during the fitting.

Multiple tool and structure analysis refers to a feed forward, feedsideways, or parallel analysis based on regression, a look-up table(i.e., “library” matching), or another fitting procedure of multipledatasets. Exemplary methods and systems for multiple tool and structureanalysis is described in U.S. Pat. No. 7,478,019, issued on Jan. 13,2009, to KLA-Tencor Corp., the entirety of which is incorporated hereinby reference.

In a further aspect, the precision and accuracy of SAXS measurementsbased on inversion of parametric models is improved based on a map of amaterial property (e.g., electron density) from the same SAXS data. Theresults of the parametric inversion are compared with the map anddifferences in the results are used to update the parameterization ofthe CD measurement model.

The distribution of the material property (e.g., index of refraction,electron density, etc.) may be used for a number of different purposes.By way of non-limiting example, the mapping may be used to 1) refine theparameterization of the physical model for model-based measurements suchas SAXS or other model-based metrology solutions, 2) flag incidencesthat are not accurately described by the model in model-based metrology,3) fix flagged values in a subsequent model-based measurement, 4) flagerrors in target alignment in six degrees of freedom, 5) determine edgeplacement errors, 6) determine the overlay error within semiconductorlayers, 7) determine the pitchwalk arising from multiple patterning, and8) estimate the values of geometric properties of a structure such ascritical dimension (CD), and sidewall angle (SWA).

It should be recognized that the various steps described throughout thepresent disclosure may be carried out by a single computer system 130or, alternatively, a multiple computer system 130. Moreover, differentsubsystems of the system 100, such as the specimen positioning system140, may include a computer system suitable for carrying out at least aportion of the steps described herein. Therefore, the aforementioneddescription should not be interpreted as a limitation on the presentinvention but merely an illustration. Further, the one or more computingsystems 130 may be configured to perform any other step(s) of any of themethod embodiments described herein.

In addition, the computer system 130 may be communicatively coupled tothe SAXS detector 116 and the SAXS illumination optics 115 in any mannerknown in the art. For example, the one or more computing systems 130 maybe coupled to computing systems associated with the SAXS detector 116and the SAXS illumination optics 115, respectively. In another example,any of the SAXS detector 116 and the SAXS illumination optics 115 may becontrolled directly by a single computer system coupled to computersystem 130.

The computer system 130 may be configured to receive and/or acquire dataor information from the subsystems of the system (e.g., SAXS detector116 and SAXS illumination optics 115, and the like) by a transmissionmedium that may include wireline and/or wireless portions. In thismanner, the transmission medium may serve as a data link between thecomputer system 130 and other subsystems of the system 100.

Computer system 130 of the metrology system 100 may be configured toreceive and/or acquire data or information (e.g., measurement results,modeling inputs, modeling results, etc.) from other systems by atransmission medium that may include wireline and/or wireless portions.In this manner, the transmission medium may serve as a data link betweenthe computer system 130 and other systems (e.g., memory on-boardmetrology system 100, external memory, or external systems). Forexample, the computing system 130 may be configured to receivemeasurement data (e.g., signals 126) from a storage medium (i.e., memory132, 180, or 190) via a data link. For instance, spectral resultsobtained using a spectrometer of any of SAXS detector 116 may be storedin a permanent or semi-permanent memory device (e.g., memory 132, 180,or 190). In this regard, the measurement results may be imported fromon-board memory or from an external memory system. Moreover, thecomputer system 130 may send data to other systems via a transmissionmedium. For instance, specimen parameter values 170 determined bycomputer system 130 may be stored in a permanent or semi-permanentmemory device (e.g., memory 180). In this regard, measurement resultsmay be exported to another system.

Computing system 130 may include, but is not limited to, a personalcomputer system, mainframe computer system, workstation, image computer,parallel processor, or any other device known in the art. In general,the term “computing system” may be broadly defined to encompass anydevice having one or more processors, which execute instructions from amemory medium.

Program instructions 134 implementing methods such as those describedherein may be transmitted over a transmission medium such as a wire,cable, or wireless transmission link. For example, as illustrated inFIG. 1, program instructions stored in memory 132 are transmitted toprocessor 131 over bus 133. Program instructions 134 are stored in acomputer readable medium (e.g., memory 132). Exemplary computer-readablemedia include read-only memory, a random access memory, a magnetic oroptical disk, or a magnetic tape.

In some embodiments, a scatterometry analysis as described herein isimplemented as part of a fabrication process tool. Examples offabrication process tools include, but are not limited to, lithographicexposure tools, film deposition tools, implant tools, and etch tools. Inthis manner, the results of a SAXS analysis are used to control afabrication process. In one example, SAXS measurement data collectedfrom one or more targets is sent to a fabrication process tool. The SAXSmeasurement data is analyzed as described herein and the results used toadjust the operation of the fabrication process tool.

Scatterometry measurements as described herein may be used to determinecharacteristics of a variety of semiconductor structures. Exemplarystructures include, but are not limited to, FinFETs, low-dimensionalstructures such as nanowires or graphene, sub 10 nm structures,lithographic structures, through substrate vias (TSVs), memorystructures such as DRAM, DRAM 4F2, FLASH, MRAM and high aspect ratiomemory structures. Exemplary structural characteristics include, but arenot limited to, geometric parameters such as line edge roughness, linewidth roughness, pore size, pore density, side wall angle, profile,critical dimension, pitch, and material parameters such as electrondensity, composition, grain structure, morphology, stress, strain, andelemental identification.

FIG. 8 illustrates a method 400 suitable for implementation by themetrology system 100 of the present invention. In one aspect, it isrecognized that data processing blocks of method 400 may be carried outvia a pre-programmed algorithm executed by one or more processors ofcomputing system 130. While the following description is presented inthe context of metrology systems 100, 200, and 300, it is recognizedherein that the particular structural aspects of metrology systems 100,200, and 300 do not represent limitations and should be interpreted asillustrative only.

In block 401, a measurement target is illuminated with a beam of x-rayradiation.

In block 402, one or more intensities each associated with one or morediffraction orders of an amount of radiation scattered from themeasurement target are detected in response to the incident beam ofx-ray radiation.

In block 403, a map of a material property of the measurement target isdetermined based on the detected intensities of the diffraction orders.The material property is any of a complex refractive index, an electrondensity, and an absorptivity of the measurement target.

As described herein, the term “critical dimension” includes any criticaldimension of a structure (e.g., bottom critical dimension, middlecritical dimension, top critical dimension, sidewall angle, gratingheight, etc.), a critical dimension between any two or more structures(e.g., distance between two structures), and a displacement between twoor more structures (e.g., overlay displacement between overlayinggrating structures, etc.). Structures may include three dimensionalstructures, patterned structures, overlay structures, etc.

As described herein, the term “critical dimension application” or“critical dimension measurement application” includes any criticaldimension measurement.

As described herein, the term “metrology system” includes any systememployed at least in part to characterize a specimen in any aspect,including critical dimension applications and overlay metrologyapplications. However, such terms of art do not limit the scope of theterm “metrology system” as described herein. In addition, the metrologysystems described herein may be configured for measurement of patternedwafers and/or unpatterned wafers. The metrology system may be configuredas a LED inspection tool, edge inspection tool, backside inspectiontool, macro-inspection tool, or multi-mode inspection tool (involvingdata from one or more platforms simultaneously), and any other metrologyor inspection tool that benefits from imaging or structures undermeasurement.

Various embodiments are described herein for a semiconductor processingsystem (e.g., an inspection system or a lithography system) that may beused for processing a specimen. The term “specimen” is used herein torefer to a wafer, a reticle, or any other sample that may be processed(e.g., printed or inspected for defects) by means known in the art.

As used herein, the term “wafer” generally refers to substrates formedof a semiconductor or non-semiconductor material. Examples include, butare not limited to, monocrystalline silicon, gallium arsenide, andindium phosphide. Such substrates may be commonly found and/or processedin semiconductor fabrication facilities. In some cases, a wafer mayinclude only the substrate (i.e., bare wafer). Alternatively, a wafermay include one or more layers of different materials formed upon asubstrate. One or more layers formed on a wafer may be “patterned” or“unpatterned.” For example, a wafer may include a plurality of dieshaving repeatable pattern features.

A “reticle” may be a reticle at any stage of a reticle fabricationprocess, or a completed reticle that may or may not be released for usein a semiconductor fabrication facility. A reticle, or a “mask,” isgenerally defined as a substantially transparent substrate havingsubstantially opaque regions formed thereon and configured in a pattern.The substrate may include, for example, a glass material such asamorphous SiO₂. A reticle may be disposed above a resist-covered waferduring an exposure step of a lithography process such that the patternon the reticle may be transferred to the resist.

One or more layers formed on a wafer may be patterned or unpatterned.For example, a wafer may include a plurality of dies, each havingrepeatable pattern features. Formation and processing of such layers ofmaterial may ultimately result in completed devices. Many differenttypes of devices may be formed on a wafer, and the term wafer as usedherein is intended to encompass a wafer on which any type of deviceknown in the art is being fabricated.

In one or more exemplary embodiments, the functions described may beimplemented in hardware, software, firmware, or any combination thereof.If implemented in software, the functions may be stored on ortransmitted over as one or more instructions or code on acomputer-readable medium. Computer-readable media includes both computerstorage media and communication media including any medium thatfacilitates transfer of a computer program from one place to another. Astorage media may be any available media that can be accessed by ageneral purpose or special purpose computer. By way of example, and notlimitation, such computer-readable media can comprise RAM, ROM, EEPROM,CD-ROM or other optical disk storage, magnetic disk storage or othermagnetic storage devices, or any other medium that can be used to carryor store desired program code means in the form of instructions or datastructures and that can be accessed by a general-purpose orspecial-purpose computer, or a general-purpose or special-purposeprocessor. Also, any connection is properly termed a computer-readablemedium. For example, if the software is transmitted from a website,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition of medium.Disk and disc, as used herein, includes compact disc (CD), laser disc,XRF disc, digital versatile disc (DVD), floppy disk and blu-ray discwhere disks usually reproduce data magnetically, while discs reproducedata optically with lasers. Combinations of the above should also beincluded within the scope of computer-readable media.

Although certain specific embodiments are described above forinstructional purposes, the teachings of this patent document havegeneral applicability and are not limited to the specific embodimentsdescribed above. Accordingly, various modifications, adaptations, andcombinations of various features of the described embodiments can bepracticed without departing from the scope of the invention as set forthin the claims.

What is claimed is:
 1. A method comprising: illuminating a measurement target with a beam of x-ray radiation; detecting one or more intensities each associated with one or more diffraction orders of an amount of radiation scattered from the measurement target in response to the incident beam of x-ray radiation; and determining a map of a material property of the measurement target based on the detected intensities of the diffraction orders, wherein the material property is any of a complex refractive index, an electron density, and an absorptivity of the measurement target.
 2. The method of claim 1, wherein the measurement target is a structure disposed on a planar substrate, wherein the structure is spatially periodic in at least one direction parallel to a planar surface of the planar substrate.
 3. The method of claim 1, wherein the illuminating of the measurement target involves illuminating the measurement target with the beam of x-ray radiation at a plurality of angles of incidence with respect to the measurement target.
 4. The method of claim 1, wherein the illuminating of the measurement target involves illuminating the measurement target with x-ray radiation at a plurality of different wavelengths.
 5. The method of claim 1, wherein the determining the map of the material property of the measurement target involves a fitting analysis of the detected intensities of the diffraction orders with a free-form model that estimates values of the intensities of the diffraction orders based on an assumed map of the material property of the measurement target.
 6. The method of claim 5, wherein the fitting analysis involves minimizing a difference between the detected intensities of the diffraction orders and the estimated intensities of the diffraction orders.
 7. The method of claim 5, wherein the fitting analysis involves minimizing a functional of the material property of the measurement target.
 8. The method of claim 7, wherein the fitting analysis involves minimizing a functional of the material property of the measurement target subject to an upper bound on a value of a difference between the detected intensities of the diffraction orders and the estimated intensities of the diffraction orders.
 9. The method of claim 5, wherein the free-form model includes a plurality of volume elements representative of the measured structure, and wherein the shape of at least one of the volume elements is changed during at least one iteration of the fitting analysis.
 10. The method of claim 5, further comprising: determining at least one specimen parameter value associated with the measurement target based on a fitting analysis of the detected intensities of the diffraction orders with a geometrically parameterized response model; and modifying the geometrically parameterized response model of the measurement target based on a difference between the map of the material property of the measurement target and the at least one specimen parameter value.
 11. The method of claim 5, further comprising: determining a value of a parameter of interest directly from the map of the material property of the measurement target.
 12. A metrology system comprising: an x-ray illumination source configured to illuminate a measurement target with a beam of x-ray radiation; an x-ray detector configured to detect one or more intensities each associated with one or more diffraction orders of an amount of radiation scattered from the measurement target in response to the incident beam of x-ray radiation; and a computing system configured to determine a map of a material property of the measurement target based on the detected intensities of the diffraction orders, wherein the material property is any of a complex refractive index, an electron density, and an absorptivity of the measurement target.
 13. The metrology system of claim 12, wherein the measurement target is a structure disposed on a planar substrate, wherein the structure is spatially periodic in at least one direction parallel to a planar surface of the planar substrate.
 14. The metrology system of claim 12, wherein the x-ray illumination source illuminates the measurement target with the beam of x-ray radiation at a plurality of angles of incidence with respect to the measurement target.
 15. The metrology system of claim 12, wherein the x-ray illumination source illuminates the measurement target with the beam of x-ray radiation at a plurality of different wavelengths.
 16. The metrology system of claim 11, wherein the computing system determines the map of the material property of the measurement target based on a fitting analysis of the detected intensities of the diffraction orders with a free-form model that estimates values of the intensities of the diffraction orders based on an assumed map of the material property of the measurement target.
 17. The metrology system of claim 16, wherein the fitting analysis is based at least in part on minimizing a difference between the detected intensities of the diffraction orders and the estimated intensities of the diffraction orders.
 18. The metrology system of claim 16, wherein the fitting analysis is based at least in part on minimizing a functional of the material property of the measurement target.
 19. The metrology system of claim 18, wherein the fitting analysis is based at least in part on minimizing a functional of the material property of the measurement target subject to an upper bound on a value of a difference between the detected intensities of the diffraction orders and the estimated intensities of the diffraction orders.
 20. The metrology system of claim 16, wherein the free-form model includes a plurality of volume elements representative of the measured structure, and wherein the shape of at least one of the volume elements is changed during at least one iteration of the fitting analysis.
 21. The metrology system of claim 16, wherein the computing system is further configured to: determine at least one specimen parameter value associated with the measurement target based on a fitting analysis of the detected intensities of the diffraction orders with a geometrically parameterized response model; and modify the geometrically parameterized response model of the measurement target based on a difference between the map of the material property of the measurement target and the at least one specimen parameter value.
 22. The metrology system of claim 16, wherein the computing system is further configured to: determine a value of a parameter of interest directly from the map of the material property of the measurement target.
 23. A non-transitory, computer-readable medium, comprising: code for causing a computer to determine a map of a material property of a measurement target based on detected intensities of diffraction orders, wherein the material property is any of a complex refractive index, an electron density, and an absorptivity of the measurement target, wherein the detected intensities are each associated with one or more diffraction orders of radiation scattered from the measurement target in response to an incident beam of x-ray radiation.
 24. The non-transitory, computer-readable medium of claim 23, further comprising: code for causing the computer to determine the map of the material property of the measurement target based on a fitting analysis of the detected intensities of the diffraction orders with a free-form model that estimates values of the intensities of the diffraction orders based on an assumed map of the material property of the measurement target.
 25. The non-transitory, computer-readable medium of claim 24, further comprising: code for causing the computer to determine a value of a parameter of interest directly from the map of the material property of the measurement target. 